# A Polynomial-time Algorithm to Achieve Extended Justified Representation

arXiv: https://arxiv.org/abs/1703.10415 · HTML: https://mlsanity.com/paper/1703.10415/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 30 Mar 2017.

## Built on by (most cited first, 1 of 1)

- [LLM Voting: Human Choices and AI Collective Decision Making](https://mlsanity.com/paper/2402.01766/) (2024)

## Abstract (arXiv)

We consider a committee voting setting in which each voter approves of a subset of candidates and based on the approvals, a target number of candidates are to be selected. In particular we focus on the axiomatic property called extended justified representation (EJR). Although a committee satisfying EJR is guaranteed to exist, the computational complexity of finding such a committee has been an open problem and explicitly mentioned in multiple recent papers. We settle the complexity of finding a committee satisfying EJR by presenting a polynomial-time algorithm for the problem. Our algorithmic approach may be useful for constructing other voting rules in multi-winner voting.